Several Variable Calculus, Limited Version
Syllabus, Bachelor's level, 1MA017
- Code
- 1MA017
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 13 May 2008
- Responsible department
- Department of Mathematics
Entry requirements
Linear Algebra and Geometry I, single Variable Calculus, Series and Ordinary Differential Equations
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Content
Polar, cylindrical and spherical coordinates. Parameterisations of curves and surfaces.
Level curves and level surfaces. Arc length. Scalar and vector valued functions of several variables. Partial derivatives, differentiability, gradient, direction derivative, differential. Derivatives of higher order. The chain rule. Taylor's formula. Optimisation: local and global problems, problems with equality constraints. Multiple integrals, change of variables especially polar coordinates, improper integrals, applications of multiple integrals: volume, centres of mass, etc. Line integrals of vector fields. Green's theorem in the plane.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2024
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Autumn 2021
- Reading list valid from Spring 2019, version 2
- Reading list valid from Spring 2019, version 1
- Reading list valid from Autumn 2016
- Reading list valid from Autumn 2012
- Reading list valid from Autumn 2009, version 2
- Reading list valid from Autumn 2009, version 1
- Reading list valid from Autumn 2007, version 2
- Reading list valid from Autumn 2007, version 1